Electrons in one dimension display the unusual property of separating their spin and charge into two independent entities: The first, which derives from uncharged spin-$1/2$ electrons, can travel at different velocities when compared with the second, which is built from charged spinless electrons. Predicted theoretically in the early 1960s, spin-charge separation has attracted renewed attention since the first evidences of experimental observation, with usual mentions as a possible explanation for high-temperature superconductivity. In one-dimensional (1D) model systems, spin-charge separation causes the frequencies of Friedel oscillations to suffer a $2k_F\to 4k_F$ crossover, mainly when dealing with strong correlations, where they are referred to as Wigner crystal oscillations. In nonmagnetized systems, the current density functionals that are applied to the 1D Hubbard model are not seen to reproduce this crossover, which leads to a more fundamental question: Are the Wigner crystal oscillations in 1D systems noninteracting V-representable? Or, is there a spin-independent Kohn-Sham potential that is able to yield spin-charge separation? Finding an appropriate answer to both questions is our main task here. By means of exact and density matrix renormalization group solutions, as well as an exchange-correlation potential introduced here, we show the answer to be positive. Specifically, the V-representable $4k_F$ oscillations emerge from attractive interactions mediated by positively charged spinless holes—the holons—as an additional contribution to the repulsive on-site Hubbard interaction.

• Received 14 December 2011

DOI:https://doi.org/10.1103/PhysRevB.86.075132